At present, mothers of 16- to 18-year-olds receive pounds 10.80 a week for a first child and pounds 8.80 for other children, but only if they are in full- time education.
Abolition of this benefit would affect about 1.1m people and save pounds 700m a year.
Mr Brown is believed to want to use these funds to support the education and training of all 16- to 18-year- olds, not just those who choose to stay in education.
His advisers cited new figures yesterday showing that four out of five children of unskilled manual workers leave school at 16 - the same proportion as in 1914 - and their mothers stop receiving child benefit.
Mr Brown, who is due to deliver the second John Smith Memorial Lecture in Edinburgh today, is expected to say: "The question is not why 35 per cent of young people now go into higher education, but why 65 per cent do not."
He will launch a passionate attack on the unfairness of access to post- 16 education and training, and is also expected to launch an attack on the Government's "one strike and you're out" approach to school drop-outs.
The savings from abolishing child benefit for over-16s would probably be channelled into "Individual Learning Accounts" for this age group.
Mr Brown and Stephen Byers, Labour's spokesman on training, recently announced plans to offer a million people grants of pounds 150 each to personal accounts which they could use to buy their own choice of training.
Mr Brown and Tony Blair, the Labour leader, are also believed to be opposed to the tax-free payment of child benefit generally to better-off parents who pay the top rate of income tax.
But senior Labour sources continue to insist that the technical difficulties of taxing child benefit rule out early action by a Labour Government.Reuse content